Some years ago, I translated a Martin McDonagh's play, "Lieutenant of Inishmore," for Japanese production. It's about a young terrorist from Inishmore island (one of the Arran Islands, Ireland) who is extremely worried about his missing pet cat. As a member of a rebel group, he kills humans cold-bloodedly, but to his little cat named Thomas, he is very very kind.
Actually, I almost forgot that the play had the missing-pet theme until I watched the DVD of the famous classic movie, "Come Back, Little Sheba" (it also was originally the play of the same title). Needless to say, its style is different than McDonagh's play, and Sheba isn't a cat, but a dog. In the movie, the couple who had the missing dog didn't mention a lot of it, although Sheba is a 'title role'. Anyway, in both "Sheba" and "Inishmore", missing pets evoke intense emotion, and play the key role while they are absent.
In Japanese literature, "Noraya" (means "Hey, Nora") by Hyakken Uchida definitely is the most famous missing-cat-themed book. It's a real story written between 1956 and 1970, in later life of Hyakken. In the form of the diary, he describes how he misses his cat named Nora that left home suddenly. As a matter of fact, nothing happens in the novel (diary?). From start to finish, he has been lamenting. But it has real poetic quality which moves us very much.
Paperback of "Noraya" with mini size Post-it (very convenient!).